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Ordinary Diff Eq Exam Review Solutions 105

# Ordinary Diff Eq Exam Review Solutions 105 - 1 Solutions 4...

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Unformatted text preview: 1 Solutions 4. A fundamental set is 107 . The matrix equation implies and . Thus , , and . Observe though that is a homogeneous solution and so the general solution can be written . The incomplete partial fraction which implies that method gives is a particular solution. The general solution is as above. 5. A fundamental set is . The matrix equation implies . Hence and , , and . The general solution is . The method of undetermined coeﬃcients implies that a particular solution is of the form . Substitution gives and hence . The general solution is as above. and 6. form a fundamental set for the homogeneous solutions. Let . Then the matrix equation implies that . From this we get . Therefore and . The general solution is . thus 7. A fundamental set is and . The matrix equation implies and . Hence, , , and . Since homogeneous solution we can write the general solution as . 8. A fundamental set is . The matrix equation implies Hence general solution is is a , and . , and . The . 9. The associated homogeneous equation is Cauchy-Euler with indicial equation . It follows that forms a fundamental set. We put the given equation is standard form to get . Thus . The matrix equation implies and . Hence ...
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